Dual strain wave gearing



July 5, 1960 c w. MUSSER DUAL STRAIN WAVE GEARING Original Filed March21, 1955 l 701 y A.

5 Sheets-Sheet l JNVEN TOR.

ATTORNEY-5 July 5, 1960 c w. MUSSER DUAL STRAIN WAVE GEARING OriginalFiled March 21, 1955 3 Sheets-Sheet 2 1 fix 0 m$ m 0 0 0 5 0 a f w u 9 om g m w 7 s w 0 r w M 0 w w 0 40 0 0 0 0 a A Wham j p a INVENTOR C Wait?mare) J ly 5, 1 c w. MUSSER 2,943,513

DUAL STRAIN WAVE GEARING Original Filed March 21, 1955 3 Sheets-Sheet 3INVENTOR a. Ma 502a M gearin'gpa nonelected 'species of myUnis-dSteamer? 2,943,513 1 f 1 DUAL STRAIN WAVE GEARING- C WaltonMusser, Beverly, Mass, assignor to United Shoe Machinery Corporation,Boston, Mass., at corporation of New Jersey Qnginal application Mar. 21,1955, Ser. No. 495,479, lviglvzd'Pategt tllziio. 2,916,143, dated Sept.29, 1959. Dian s a ti i 656,572 pp ca on May 2, 1957, Ser No .118Claims.(Cl.7=4-6'40) I The present invention relates to motion transmittingmechanism, and particularlyto gearing in which relative motion occursbetween an internal gear and a cooperatlng external gear. i

The present application relates to dual strain wave 7 application SerialNo. 495,479, filed March 21, 1955, for Strain Wave Gearing, now US.Patent No. 2,906,143, granted September 29, 1959.. The reader isreferred to this patent for an understanding of the background and thebasic principles which are involved in the present invention.

A purpose of the invention is to produce a very compact, convenient andinexpensive form of strain wave gearing by employing a strain gear whichfunctions as a-common element in cooperation with a plurality ofdifferent ringgears and is deflected to propagate a strain wave withresp ect to the plurality of different ring gears. fin-further purposeis to secure a wide variety of available gear reductions by variationsin gearing of the same design; and especiallyto'obtain very large gearreductions. i v

A' turther purpose is to obtain gearr-atios' in the range between -1-0to "1 and 1' million mi from a gearing'system.'

Afurther purpose is to obtain a very wide and preferably unlimited ratioselection.

1 l p Pa e te -Mk 1.

I pQt to a developed deflection circle as the ab scissa'. j

Figures a and 10b are diagrams which illustrate the shape of the toothfor a linear relation between deflection and revolution.

Figures 11 and -12 are fragmentary axial sections of variousarrangements of thecomponents in dual strain wave gearing according tothe invention.

Describing in illustration, but not in limitation and referring to thedrawings:

GENERAL FEATURES oF INVENTION The present inventionis' concerned witheliminating difficulties. encountered in conventional gearing, as willdeals particularly with gearing of a'character in which inner and outerconcentric gears are brought into mating relationship in a plurality ofspaced areas with interspersed areas in which they are not in matingrelationship, and the areas of mating relationship are propagatedforward in a wave which for the purposes of the present invention isdescribed as a strain wave, since it represents a wave deflection in oneof the gearing elements.

This strain Wave is I actually superimposed on the circumference of oneor both of the gears, and travels with respect to it at a rate which isdetermined by the rate of application of load or rotatory force to themechamsm.

It should be appreciated'thatin the mechanism oi the present invention,unlike all ordinary gearing, cooperating gears move into and out oftooth engagement by radial motion ofthe'teeth oione' gear with respectto the other,

A further purpose is to construct a motion transmitting Y device havinga first ring, a secondring, and athird ring of different diameterfromthe first and secondtring, concentric therewith 'and'having adeflectable wall, and'having a strain inducing-elementinengagement withthe third ring and maintaining the third ring'deflected into matingrelation with the first and second ring at a plurality ofcircumierentially spaced positions interspaced by a nonmating position,and having means for moving the strain inducing element relative to theperiphery of the third ring and thereby-propagating a strain Wave aroundthe periphery of the third ring and causing relative rotation of thesecond'ring with respectto the first ring.

Further purposes appear in the specification and in theclaims." In thedrawings I have chosen toillustrate a few' only of: the numerousembodiments in which'iny invention without in the leastfnecessitatinganychange in the gear axis. It viiillfbe-eyident, therefore, that actionpre supposes a motion Qf'partsof one'of' the, gears wanna-- specttooth'erparts hich'canbeaccomplished inany t suitable manner; bupreferably will' 'be achieved by jdis torting an elastic material; whichmaybe for example an 'elastofrner ch as rubber, synthetic rubber, nylon,or

gear ma erial, moving 'thin-the elasticlimit, and there?by-s'ubst'antially free from plastic defo nnation. 'While'inthe'ibroadest a'spects,'the invention is applicable to rings whichfrictionally engage, as Wellas to elements having tooth engagement,andf-While it is also I applicable to" straight elements having toothengagement tion, and cleardemonstrationbf the principles involved.

Figure 1 is an exploded axial section of a device for transmittingmotion according to the present invention;

inasimplifiedfo-rm p Figure 2 is a right end elevation of the straininducer shown in Figure '1. e Figure 3 is an axial seetion correspondinggenerally to the exploded section of Figure 1, but showing the partsassembled in their normal operating relationship. j Figure 4 is a rightend elevation of the assembly of Figure 3.

Figure 5 to 8 inclusive are enlarged developed fragmentary sectionstransverse to the axis showing the relative relations of the teeth atvarious positions in Figure 4, as indicated by the corresponding sectionlines.

Figure 9 is a diagram showing strain wave as ordinate Figure 9.

which are 'distorted t'omate and propagate a strain wave, likecooperating rackelements, it will'be'evident that the invention isbelieved to have its widest application in relatively -internal andexternal gears,'-one of which 'is distorted at a plurality of points tomate with the other cooperating gear; f l It will, "however,be-understo'od that the principles of the invention are applicable-t0any suitable mechanism" which applies 'the p'ropagated wave inducingmating engagements acoording toth'edisclosure of the invention. I 1. .,PN I SIQF' R N' Strain wave'geai'ing is "a novel system for transmittingniotion and power, in which'the gear tooth engagement is induced at -aplurality of points bythe deflection of a thin ring gear or the like.The toothengagementat a plurality "of points-around the circumference ispropagated 'al-on'g tlie periphery of the thin ring gear as the crest ofthefinduced deflection Wave is made to move around this periphe'ry; Asthe deflection moves around the gear, each tooth moves radially inandout of engagement-as it progresses from one tooth-t0 the next, tracingduring. this motion a curve which is generally of the character of -asinusoidal wave,* givingrise to the term; strain wave gearing? Such awave is illustrated in 'etaIsuclr asQste'el, 'bronie, or other" Inthe'simplest form as'sliown for example in Figures 1 to 8 inclusive, themotion transmitting device consists of a ring gear 70, a strain gear 71,and a strain inducer 72. The ring gear has internal teeth 73 in theillustration shown, which are preferably of axially extending character.In this form the strain gear 71 has external teeth 74 which alsopreferably extend axially and at the same diametral pitch as the teethon the ring gear but have a slightly smaller pitch diameter. Thisdifierence in pitch diameter is caused by the fact that the number ofteeth in this case on the strain gear is less than the number of teethon the ring gear. The difierence in the number of teeth between the twogears, or the tooth diflerential, should be equal to or a multiple ofthe number of places at which the strain gear is deflected to causetooth engagement with the ring gear. This differential would desirablybe two using a strain inducer having an elliptical contour with twolobes 75, as shown in Figures 1 and 2. As already explained, the straingear 71 is made of a material which is elastic under the conditions ofoperation, and in the case of a steel strain gear, is made of relativelythin cross section so that it can be deflected easily in a radialdirection.

The form of strain inducer for transmitting motion as illustrated inFigures 1 to 8 is a very simple one having two points of strainengagement of the strain gear. The strain inducer 72 has an ellipticalcontour, as already explained, whose major axis A is larger than theinside diameter of the strain gear 71 by an amount approximately equalto the difference in pitch diameter of the ring gear and the straingear. The minor axis B is smaller than the inside diameter of the straingear by approximately the same amount. When the strain inducer isinserted into a position inside .the strain gear, as shown in Figure 3,it causes the strain gear to be distorted into elliptical form, with thepitch line of the teeth at the major axis equal to the pitch'diameter ofthe ring gear as shown at'76 in Figures 4 and 8 At the position as shownin Figure 8 the pitch circles of the two gears are coincident.- At theminor' axis the pitch line of the strain gear teeth is smaller than .the,pitch diameter of the ring gear, and if ;a full tooth height is used,the teeth will just clear'one another as shown at77 in Figures 4 and 6.At intermediate points 78' and 80 as shown in Figures 4, and 7, theteeth will have varying degrees of engagement. This condition prevailswhere the tooth differential is equal to the number of lobes on thestrain inducer which in this case is two.

Figure 9 plots a curve for a strain gear having a two lobe straininducer. There are therefore two complete waves in 360 or one completerevolution. The ordinate is tooth engagement in 0.001 inch and the-abscissa is degrees in the revolution. The height of the wave is equalto the total deflection. This is referred to as tooth engagement becauseit is this up and down or actually radial in and out motion thatproduces toothengagement and disengagement in circular strain -wavegearing. Straight lines are superimposed on the two sides of the of acircle, and height of the total wave or the deflection is approximatelytwice the radial displacement of the peaks of the wave from this circle.If it were plotted in this manner, the deflection for that portion ofthe wave having a greater radial distance from the center than thecircumference would be given as plus strain. The other portion of thewave having a lesser radial distance would be given as minus strain. Theposition before strain (or the circumference of the relaxed ring) isindicated in Figure '9 as the undefleeted position. How.- ever, it willbe evident that measurement of the wave and all of the calculations aresimplified by considering the total deflection as being measured from abase line coinwave to obtain the closest possible match over as great apercentage of the distance as possible. When the height of the triangleformed in this manner'is 1.44 times greater than ;the deflection, thematchover more than 50% of the curve is within: 0.00025 inch. This isexplained in detail inrefeIence to my prior Patent No. 2,926,143 abovereferred to.

. The dots shown in Figure 9 .on the strain wave are plotted from actualdata measured from a strained ring. These dots also show the progressivemovement of the teeth on a strain :gear with movement of the straininducer. This wave .of .course ;is purposely exaggerated in height toproperly illustrate the wave shape and facilitate accurate plotting; EIfthe degrees (revolution) were shown to the same scale as the deflection,the wave would be approximately 71.25 times as long as illustrated. Thiswave at any instant is superimposed on the circumference cident withthat portion of the wave which has the least radial distance from thecenter.

It will be evident upon analysis that the shape .of the wave drawn to abase line equal in length to the circular pitch, that is, the distancefrom one tooth to the next, will accurately outline the tooth form. Whendrawn to these proportions the wave looks essentially as shown in Figure9, with the abscissa equal to the circular pitch for two teeth. In orderto illustrate this relationship, the deflection wave shownin Figure 10ais represented as a linear function of revolution. The deflection ismade exactly equal to the tooth height as shown in Figure 1012. Thus itwill be seen that a revolution of a two lobe strain inducer in strainwave gearing produced according to these proportions will cause a changein radial deflection equal to the tooth height ,for the teeth that wereeither fully engaged or fully disengaged.

For properly shaped teeth, of the teeth under this condition would be incontact, but in various degrees of engagement. Proceeding from the baseline in Figures 10a and 10b, or from the disengaged position, one sideof the teeth on the strain gear will become progressively more engagedwith one side of the teeth on the ring gear as the apex of the curve isapproached. At the point of 45 9 revolution, the teeth will be engaged50% or deflection/ 2, At 90 revolution they .will be fully engaged.Proceeding beyond 90", the teeth will become progressively less engagedon the. next 90 revolution. Here, however, the

opposite side of the tooth is in contact. It is an unusual feature ofthe gearing of the present invention that fol T1116 same direction ofdrive successively opposite sides of the same tooth engage as the teethadvance.

Hence for 90 revolution the phase relationship of the teeth changes orit is one-half tooth out of phase. This accordingly indicates that theteeth, for this shape of strain wave, should be equal in height to thedeflection and have a base line equal .to the out-of-phase relationshipfor 180 revolution. The included angle is determined by thisrelationship. The sides of this angle are straight since the deflectionchosen has a linear relationship with revolution. Consequently the curveof Figure 10a is fully representative of tooth form if the abscissaisequal to the circular pitch of one tooth.

From Figure 10 it is possible to produce a generalized formula forcircular pitch for use in strain wave gearing calculation. Thenomenclature as applied to this .calculation and as appearing on Figure10 is as follows:

qThen nP N'EP therefore the circular pitchtormula for strain wavegeariiigis' i it Here thecircular pitch is reduced to a definiterelationship with deflection and number of lobes on the strain inducer.As a result, the tooth form isdependent only 1 .Dueto the differentialaction between the two gears, large gear reductions are easily obtainedwithout multiplicity of parts; One of the means of calculating gearratio is'the pitch diameter of the driven gear divided by the.deflection- Since the deflectioncan be made very small, the gear ratioscan be made very large without sacri- V ficing the other advantages ofstrain wave gearing.

High e/ficiency fbrihigh gear ratio e efliciency of strain wave gearingis discussed in my ii.S.'Patent No. 2,926,143 previously referred to. Itwas y there shown that a gear system with a ratio of 100 to 1had-an;over-allefliciency between 69 and 96'percent dependingonworkmanship and'lubrication. Increasing the ratio does 1 not decreasethe. efficiency as markedly 1 e 'coeflicients. of friction and the sametype straininducerare used, .a-400 to 1 ratio gear system'will have an80 percent efiiciency in :relationJto 93;percent efiisn y or a 0 Q:. yhe u of a d fie e p train ilindusen moras nimb f r e g er at theefiiciency of the 400 to :1; ratio ,systemwill be'88 percent,

It has been, experimentally ascertained that a 300 to 1 ratio strainwave gear system built intoag motor'had an efii ciency in excess of75'percent when tested under the adverse condition of light loading.

'Small size As indicated above in regard to thelarge torquecapabilities, '"aj' s'tfrain*wave gear reducer hasa large capacityforfgii'ren -size. As a consequencefa unit for the same capacit M ouldhe "relatively" yery small'in size. Calculat ion s' 'indicate that,excluding" the question or thermal capacity, a strain wave gear reducerWould'be less than IO-perCent cubic size" of that of a standard gea'rreof ui nent ratio and torque capacity; iRgtisjram lo to1Jt0,1,000,000jw1 y V Deflection and diarheterare the determinants ofgear ratios from:about25 to.;1 to to 1 thepro'per grade of rubberorneoprene may belused :to advantage.

I .1 iiwhereit is desired to increase the ratio beyond approximatelya200 to lyarball or;r'o11er.strai inducer is used.

the case instandard gearing. If the same easily ata The"? strain wave-3sgenerated by the. individual balls :or.

rollers :which. have -a planetary-reduction relationship. to

the ,su'n"inner raceway; InaorderLto obtain the overall ratio, the ratio'ofthe'strain wave" gear is multiplied by the planetaryreductionrelation of the planet rollerswith thesun: inner raceway. Ratios up to1000 to 1 can easily be'obtained by this method without any increase incomplexity. s 1

For ratios from 1000 to 1 to 1,000,000 to 1', dual strain wa'vegearingis used. With this there are always-gearsinstead of the:usua1 two;astationary ring geanamovable driven ring gear and=a strain gear. Thetwo ring gears are keyed together by thedeflected strain gear. Theoperation of.dual strain wavegearing is described below.

7 V Ratio selection not limited Usually in differential mechanisms whereteeth are used, ratios frequently are in steps and the ratios in between7 these steps can only beobtained by compounding. The

ratios of toothed strain wave gearing, also, must of necessity' beinsteps. However, these steps are considerably smaller and are withoutvoids. For example, the ratio can be stated simply as the number ofteeth in the driven gear divided by the number of lobes on thestraininducer. Then 'for a three lobe strain inducer, ratios'can be made tochange in steps of one third. When the planetary strain inducer is used,this can be further divided to obtain any gear ratio desirable;

' BASIC FORMS The reader is referred to the patent above referred to fornumerous examples of difierent types of strain inducers which can beemployed in the present invention.

For some purposesit is desirable to obtain gear ratios which aresubstantially higher or substantially lower thanthose which'can beconveniently secured from standard or inverted strain wave gearings ofthe single type. For

such purposes dual or higher multiple strain wave gearing will be used.Illustrationsof this are shown in Figures 11 and-12. 1

In Figure 11, there are twostages of strain wave gearing arranged in onehousing. ---Ring gear at one side is secured to housing 151 whihi'sdesirably stationary. The

ring gear 150 meshes with external teeth 152' on oneend of strain gear152, under the action of strain inducer 153 which is turning with shaft154 by which the input load is applied. The strain gear 152 at alongitudinally displacedposition, has external teeth 155 which are actedon interiorlyby the same strain inducer, and which exteriorlymeshwithsecond internal ring gear 156 which has hearing support at157onfthehousing and is conveniently integral with the output shaft'158.The two sets of teeth on the strain gear are made with a maximumdifierence of a few teeth so that they do not diifer greatly in pitchdiameter. Consequently the difierence in' the deflection is so smallthat only one strain inducer is required and the twosets can be combinedin a single ring without the need for substantial axial displacementbetween one set and another to allow for relative adjustment byflexibility of the intermediate tube.

It will be understood, however, that if the xaial displacement-betweenthe two sets'of teeth on the strain gear is adequategthere can be widedisparity in the strain in-- ducers, for example, one having :two lobesand the other celling the rotation of the driven gear. For example, if

the strain inducer 154 is rotated clockwise in Figure 11,

. the straingear S .or 152,:will rotate in'theoppositeidirec tion1;orcounterclockwise. ,At the same..time,'-the.otl1'er strain gear integraltherewith S or 155 is tending "to drive the driven gear 156 thesameadirectionas thestrain inducer or clockwise. Consequently .one addsand theother subtracts from the overall motionand by correctly determining thedifference in the number of teeth, the very high gear ratios can beobtained. V

This relation can best be shown by reducing each strain wave gear to itsown specific gear ratio. 'Any suitable formula in Table 2 in said patentcan be used for this purpose if we remember that the gear with thelargest number of teeth turns in the same direction as the straininducer. Since multiplication, addition, and subtraction enter into thecalculations for dual strain wave gearing, it is mandatory that we useproper signs in designating directions. If the movement is in the samedirection as the strain inducer,it is considered plus. If'the movementis opposite to that of the strain inducer, it is considered minus. Onesimple method of always obtaining the proper ratio and sign is to dividethe diameter of the gear being driven by the diameter of the gear beingdriven minus the diameter of the mating gear. When this is done thedivisor will always be negative when the gear being driven has thesmaller diameter, thus producing a negative or opposite direction gearratio.

Applying this analysis to Figure 11, it will be evident that onerevolution of the plain bearing strain inducer will cause the straingear S to rotate the reciprocal of the ratio and sincethis rotation isin the opposite direction the result is i Since thestrain inducer hasrotated one turn to its original 7 position and the strain gear S hasmoved the strain inducer has moved Gonsequently, the motion of thedriven gear D would become strain inducer and the strain gear S As thetwo strain gears are coupled together, the motion of was must be addedto R =Ratio of driven side R =Ratio of fixed side With 1 revolution ofthe strain inducer I S rotatesrevolutions and the strain inducerhasrotated 1 plus in relation to S The reciprocal of this, shown above inFormula 1, would be equal to the overall gear ratio. It the proper signsare considered, the formula can be stated simply the product of theratios divided by the sum of the ratios minus 1. This basic formula isshown below in Formula 3 and it is correct for all forms of dual strainwave gearing. Formula 2 applies specifically to' dual strain wavegearing of the type of Figure 11, and was calculated by other means as acheck on the above analysis.

Figure 12 illustrates a dual combined strain wave gear. Over at theright the construction substantially resembles that of Figure 11, exceptthat the strain inducer extends inside only one side of the strain gearand the strain gearv has external teeth which extend the full length andengage a correspondingly elongated ring gear At the opposite end fromthe strain inducer the strain gear has internal teeth which mesh with anexternal driven gear 161 carried on the output shaft 158.

In effect, one side of the device is a standard'strain wave gear formand the other side is' an inverted form. The strain inducer producesdeflection of the strain gear which causes the strain Wave to act bothin respect to the external teeth and the internal teeth in the mannerabove described. This arrangement is useful for very low gear ratios ofthe order of 30 to 1 when produced with steel, small diameter strainwave gears. I I

The following formulae were developed by analysis of the motions ofthese gears after the manner of that already described in respect toFigure 11: 5

It will be evident that Formula 3 differs from Formula 1 only in respectto the sign of the ratio. It theproper signs are considered whencalculating the individual ratios, basic Formula 4 may be used for gearsof any of the dual strain-wave types. =i

It will likewise be evident that while strain inducers of a mechanicalcharacter have been illustrated,,the strain wave can be applied by anymeans, whether electrical, magnetic, hydraulic, pneumatic, orvibratorywhich will generate and propagate a progressive strain wave.

In view of my invention and disclosure, variations and modifications tomeet individual whim or particular need will doubtless become evident toothers skilled :;in the art to obtain all or part of the benefits of myinvention without copying the structure and method shown, and I,therefore, claim all such insofar as they fall within the reasonablespirit and scope of my claims. Having thus described my invention, whatliclaim' as new and desire to secure by Letters Patent is:

1. In a device for transmitting motion, a train of two sets of gearingeach including a first gear having teeth, a strain gear having teeth ofthe same size as those onthe 7 9 first gear interconnecting the twosets, the strain gear being of dilferent diameter from the first gear,concentric therewith and having a deflectable wall, a strain inducingelement operative to deflect the strain gear and maintaining the straingear deflected into mating relation with the first gear on theconcentric axis at a plurality of circumferentially spaced positionsinterspaced by non-mating positions, and means for moving the operativerelationship of the strain inducing element for each gearing set of thetrain relative to the periphery'of the strain gear and therebypropagating a strain wave around the periphery of the strain gear andcausing relative rotation of the strain gear with respect to the firstgear.

2. A device of claim 1, in which the strain inducer is common to the twosets of gearing of the train.

3; A device of claim 1, in which the strain gear has two sets of teethdirected in the same radial direction.

4. A device of claim 1, in which the strain gear has two sets of teethdirected in opposite radial directions.

5. A device of claim 1, in which there are diiferent numbers of teeth inthe teeth sets on the strain gear operating in the difierent gearingsets.

6. A device of claim 1, in combination with a housing, one of the firstgears being secured to the housing, another of the first gearsconstituting either the input or the output and the strain inducerconstituting either the output or the input.

7. A device of claim 6, in which the strain gear has two sets ofexternal teeth, and the strain inducer operates inside both sets.

8. A device of claim 6, in which'the strain gear has one set of externalteeth and one set of internal teeth, and

the strain inducer operates inside the set of external teeth to one sideof the set of internal teeth.

two diametrally-opposed mating positions.

10. A device :of claim 1, in which the mating gears 9. A deviceof claim1-,' in which the mating gears have genie 1s 10 14. A device of claim 1,in which the teeth of the first gear and the strain gear conform to thefollowing formula:

'strain gear, and cooperates with the external teeth on the strain gearand the strain inducer is positioned inside .the strain gear, incombination with a further gearrinside the strain gear having externalgear teeth which make strain wave engagement on the strain gear.

16. A device of claim 1, in which the strain gear and the first gearhave cooperating gear teeth of the same diametral pitch but of differentpitch diameter and in which the number of teeth on the strain gear andthe first gear diifer by a quantity which is equal to or a multiple ofthe number of lobes on the strain inducer.

17. A gearing system including a plurality of interconnected sets ofmeshing gears and means for straining one of the gears of each set intoengagement with another and thereby creating a strain wave, the gearshaving different numbers of teeth and the difference between the numbersof teeth on the respective gears equalling the number of strain wavesper circumference.

18. In a device for transmitting motion, a first gear, a strain gear ofdifferent diameter from the first gear, concentric therewith and havinga deflectable wall, the strain gear having two sets of axially displacedgear teeth on its outside, and the first gear being provided withinternal teeth surrounding the strain gear'and cooperating with one ofthe sets of teeth on the strain gear, a strain inducing element insidethe strain'gear, operative to dehave three generally equalcircumferentially spaced mat- 7 ing positions. p v

1-1. A device of claim 1, in which in one of the gear sets the firstgear is positioned inside the strain gear and element comprises araceway in contact with one circumferential surface of the first gear,and means including bearing elements travelling in the raceway forpropagating a strain wave against the wall of the raceway.

' the external surface "of the first gear engages the strain fiectthestrain gear and maintaining the strain gear defiected into matingrelation with the first gear. on the concentric axis at a plurality ofcircumferentially spaced positions interspaced by non-mating positions,a second gear surrounding the strain gear and in cooperative relationwith the otherv of the sets of teeth on the strain gear, and

means'for moving the operative relationship of the strain inducingelement relative to the periphery of the strain gear and therebypropagating a strain wave around the periphery of the strain gear andcausing relative rotation of the second gear with respect to the firstgear.

No references, cited.

